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The talks started in training camp. Danny Ainge had convinced Doc Rivers to come back and coach the Celtics for at least one more season, make one last run at a title with a team that came within minutes of winning it all in Los Angeles.

Ainge wanted to offer Rivers an extension immediately. Stay on, become an institution like Gregg Popovich has been for 15 years as coach in San Antonio. Like Jerry Sloan was for 23 years in Utah.

At that point, Rivers had family concerns. One son, Jeremiah, was about to start his basketball season at Indiana University. Another son, Austin, was the country’s top high school prospect, who’d be Duke-bound in a matter of months. His daughter, Callie, was a senior at the University of Florida, playing volleyball. His youngest, Spencer, was still at home in Winter Park, Fla.

Beyond that, there was the obvious matter of burnout. From the title run in 2008, to the deflating and injury-stunted 2009 push, to the agonizing end to 2010, the past three seasons had been emotionally exhausting and mentally demanding.

Rivers wasn’t ready to commit. Ainge didn’t press, but he continued talking.

“[Rivers] didn’t really want to be distracted early in the year,’’ Ainge said. “He wanted time, and I left him alone.’’

The conversation picked up during the middle of the season. Then died down. They talked again as the playoffs were about to begin. Then the perfect window opened up: a weeklong postseason break between series with the Knicks and the Heat.

There was also a catalyst in the form of Celtics ownership.

“Danny had been talking to him all year about it,’’ said co-owner Wyc Grousbeck. “I really wanted to accelerate it before the end of the year, because I didn’t want to go into the postseason and have uncertainty. I wanted to lock him down.’’

That week, Ainge talked to Rivers and his agent, reaching a gentlemen’s agreement, a handshake more or less. But that’s all they needed.

When the Celtics were eliminated by the Heat Wednesday night, Rivers was all but certain he’d be back for another season, saying, “I’m a Celtic.’’

The contractual details were a formality that was settled upon yesterday when Rivers agreed to a five-year, $35 million contract extension, calling Ainge in the morning just as he was walking to meet the media.

“They got the deal done,’’ Grousbeck said.

Rivers has a mountain of milestones from his seven years in Boston. In 2007-08, he got Ray Allen, Kevin Garnett, and Paul Pierce to buy into Ubuntu and bring the city its first championship since the Larry Bird era. His 336 wins are the third most in franchise history behind Red Auerbach (795) and Tom Heinsohn (427).

The common opinion was whenever Rivers decided he wanted to leave the Celtics, he could pick his next coaching job.

“I think Doc is the best coach in the league, so I think it’s great for us to have him around,’’ Ainge said. “There have been times over the last couple years I thought he was going to leave. I would have understood if he left. But we’re glad that he’s not.’’

At the start of the season, Rivers had to shoot down rumors he would coach the Heat should Erik Spoelstra not work out in Miami. Rajon Rondo and Allen both said they could see it, Rivers getting Miami’s three stars to align the same way he did in Boston. Rivers’s name had also been tossed around as a replacement for the retired Phil Jackson in Los Angeles. But Grousbeck said securing Rivers for the long term had less to do with playing keep away with a hot commodity and more to do with keeping a proven one.

“Doc’s a great talent and we locked him in for five years,’’ Grousbeck said. “It’s just building positively. It wasn’t a defensive move. It’s not about him going anywhere else. It’s about having him here. When we see somebody we like, we want to go out and do it. It’s about trying to keep quality people at the Celtics.’’

Rather than let the process drag out, Rivers came to his decision quickly. Last summer, he took two weeks to decompress after the Celtics’ loss to the Lakers in Game 7 of the Finals.

“Last year when Doc was sort of contemplating whether he wanted to stay or not, I think those were more family issues,’’ Ainge said. “He had to resolve some things in his own mind with family. We tried to do a contract extension then, but we were just not on the same page and we were in more of a rush.

“He just wanted to come back this year and see how it was going to be. So we just did a one-year contract . . . But Doc has always known that we wanted him and that an offer was on the table.’’

Next season will be unlike the past four. Allen, Garnett, and Pierce won’t be able to solely carry the team to a title. The team will have to add pieces that can run down loose balls and play above the rim. The Celtics are regrouping. Not only is Rivers willing to rebuild, but management knows he’s also equipped to do so. He won coach of the year in 2000 for Orlando with four undrafted free agents.

“Doc is interesting,’’ said Celtics co-owner Stephen Pagliuca. “I think of all coaches, he’s been one of the few that’s actually done a fantastic job during a rebuilding stage and done a fantastic job when we’ve had a championship team. So Doc is built to coach. He’s a teacher, he’s a coach. But he’s one of the few coaches who have done both. That’s unique, because that’s two different skills.’’

The 24-58 season in 2006-07 that some view as a blemish on Rivers’s résumé — some fans were calling for Rivers to be fired — is where Pagliuca said the bond was established.

“I think you develop a trust with people and we developed an immediate trust with Doc,’’ Pagliuca said. “When we lost over 50 games, I think Danny and the whole ownership group, we were steadfast in that we knew we had a great head coach and a great general manager.

“The knee-jerk reaction is to blame the losses on the coach, but the coach was doing an excellent job with the players we had left and we were competing in every one of those games. I think in the bad times is where you develop trust.

“It’s easy to develop trust in the good times. You’re winning, you think that’s the way it’ll be and there will be no questions. But in the bad times, that’s when you develop trust and I think that’s when it was developed over that time, both ways.’’